I evaluated the Mach-number equation given by r.d. baertschiger below:

M= sqrt[ 5 [({ [( 1 + 0.2 [ 350/661.5 ]^2 )^3.5 -1 ] [ 1- ( 6.875^1E-6 ) 25500 ]^-5.2656 } +1 )^0.286 -1 ] ]

using a number of diiferent machines.

**RESULTS**

-- RPN (12C, 15C, 17Bii, 28S, 48G, 49G):

I got the correct answer (0.835724536) every time within one minute of work, once I saw how the expressions nested (match the braces "{}" by multiplying two long results.)

-- Non-symbolic AOS __with__ precedence (20S, Casio fx-3600p):

I got the correct answer on the first try with somewhat more time, when entering the expression exactly as written, which utilizes precedence. Doing the ()'s slows one down a little.

-- Symbolic AOS __with__ precedence (28S, 48G, 49G):

I got the correct answer on the first try, but required more time, due to all the "()". This method gives no intermediate results, however, so the final answer must almost be accepted on faith, unless one scrutinizes the symbolic expressions after-the-fact.

-- Symbolic AOS __without__ precedence (17Bii):

Serious difficulties getting the correct answer, with repeated failures. Extra ()'s must be inserted at the right time to handle lack of precedence, and if it wasn't done, it's difficult to fix.

-- Non-symbolic AOS __without__ precedence (10B):

Repeated failures required completely starting over, and ()'s were shifted. Horrible!

-- Equation writers/editors (48G, 49G, 17Bii):

Very cumbersome; expressions were hard to read. Many failures. 48G equation writer could not keep up with user input.

**FINAL VERDICTS**

-- RPN:

Probably best for correctly solving this type of problem, because you see all intermediate results, and you know what they represent. Error recovery is easy. Of course, a strategy for evaluation must be devised beforehand, but RPN users are good at it.

-- Non-symbolic AOS with precedence:

Also useable, but the intermediate results produced by ")" are less obvious. (How many operations were performed, and what were they?) The user can enter the problem exactly as written, but it must be written according to the rules of precedence. "Fixing" the calculation midstream is nearly impossible.

Instead of entering the experssion left-to-right, a quasi-RPN approach can be emulated with liberal use of "=" and storage registers.

-- Symbolic AOS and equation writers/editors:

Allows the user to see the complete expression, but not the intermediate results upon evaluation. I wouldn't trust 'em.

- AOS without precedence:

Leave 'em for the business people!